Speed of sound bounds and first-order phase transitions in compact stars

In the present study, we employ three distinct, physically motivated speed of sound bounds to construct hybrid models, where the high-density phase is described by the maximally stiff equation of state. In particular, we consider the bounds related to special relativity, relativistic kinetic theory and conformality. The low-density hadronic phase is described by a state-of-the-art microscopic relativistic Brueckner-Hartree-Fock theory. This work aims to access the effect of the different speed of sound constraints on the relevant parameter space of the key parameters of first-order phase transitions by utilizing recent astronomical data. This involves a systematic analysis that also includes two distinct schemes for the construction of hybrid models (abrupt and smooth). Finally, a relevant discussion is conducted on the possible occurrence of a thermodynamic inconsistency that is related to the stability of the high-density phase over hadronic matter at large densities.